Investigation of the mean free path of projectile fragments produced in 16O－Em collision at 60 A GeV

Results are presented for an investigation of the mean free path of projectile fragments with charge 3≤Z≤8, produced by 60 A GeV {}^{16}O in nuclear emulsion. No dependence of mean free path on the distance from the point of the fragment emission is observed and our result is consistent with the nonexistence of anomalons.     

Sandwich-type transition metal complexes [(CBO)n]2M with carbon boronyl ligands (CBO)n (n=4–6)

A density functional theory investigation on a series of sandwich-type transition metal complexes [(CBO)_n]₂M (n=4–6; M=transition metals) with carbon boronyls (CBO)_n as effective aromatic ligands has been presented in this work at B3LYP level. The ground-states of these complexes possess staggered D_nd symmetries, while the corresponding eclipsed D_nh structures exist as transition states with slightly higher energies (within 5.8 kJ/mol). Carbon boronyl complexes [(CBO)_n]₂M are confirmed to be much more stable than their boron carbonyl isomers [(BCO)_n]₂M, which, on the other hand, take eclipsed ground-states with D_nh symmetries. The carbon boronyl complexes [(BCO)_n]₂M proposed in this work parallelize the well-known sandwich-type hydrocarbon complexes [C_nH_n]₂M in coordination chemistry with boronyl groups –BO isolobal to –H atoms in corresponding ligands.     

Level surfaces of non-degenerate functions inR n+1

We study level surfaces of non-degenerate functions inR ⁿ⁺¹. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field for level surfaces of a non-degenerate function and give certain characterizations of when is transversal, by the shape operatorS, the transversal connection , and consider the difference between and the affine normal.     

Tetradecker transition metal complexes containing double planar hexacoordinate carbons and double planar heptacoordinate borons

A theoretical investigation on tetradecker transition metal complexes of Cp-Fe-CB6-Fe-CB6-Fe-Cp (1) containing double planar hexacoordinate carbons and Cp-Fe-BB7-Fe-BB7-Fe-Cp (2) containing double planar heptcoordinate borons has been performed in this work at density functional theory level. [CpFe]+ monocations prove to effectively stabilize these unusual complexes, which are mainly maintained by effective d-pi coordination interactions between the partially filled Fe 3d orbitals and the delocalized pi molecular orbitals (MOs) of the four planar deckerlike ligands. The results obtained in these model computations expand the domain of ferrocene chemistry and could provide a new approach for synthesizing planar hyper-coordinate carbons and borons in transition metal complexes.     

Production of helium projectile fragments in {16O－emulsion interactions at 4.5 A GeV/c

The measurements of partial production cross sections of the multiple helium projectile fragments emitted at 4.5 A GeV/c {}^{16}O－Em interactions are reported. We have studied the production rate of helium projectile fragments due to fragmentation of {}^{16}O ions and compared it with that obtained from different projectiles at various energies. The dependence of on the mass number of the incident beams is formulated. The multiplicity distributions of the helium fragments produced in {}^{16}O－Em interactions at different energies exhibit Koba－Nielson－Olesen (KNO) scaling. The correlation of helium projectile fragments and target fragments is also investigated and it is found that the average of target fragments is increased with the decrease of the number of helium fragments in peripheral interactions.     

Fragmentation of ^16O nuclei in nuclear emulsion

We present the topology of 16O fragmentation at 60A GeV in reactions with emulsion nuclei.We discuss the multiplicity distributions of projectile fragments.charged secondaries and their dependence on the target residues.     

Existence of solutions to a class of nonlinear second order two-point boundary value problems

In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u^″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u^′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role.     

C2h (BnEmSi)2H2 molecules (E = B, C, Si; n = 3-6; m = 1, 2) containing double planar tetra-, penta-, and hexacoordinate silicons

A density functional theory investigation on a series of S-shaped or cyclic (BnEmSi)2H2 molecules (E = B, C, Si; n = 3-6; m = 1, 2) containing double planar tetra-, penta-, and hexacoordinate silicons has been presented in this work. Further theoretical evidence is provided to support the previously proposed structural pattern to host planar hypercoordinate silicons in small aromatic molecules.